Systems and methods disclosed herein improve the quality and speed of computing deformations used to animate artwork. One aspect provides adaptive meshing that creates a mesh adapted to handle locations and weights associating the handles with the mesh vertices. Portions of the mesh requiring smaller triangles with more densely positioned vertices are identified based on the handle locations and associated weights and resolution is added only to those portions of the mesh in which finer resolution is required. A second aspect involves creating a mesh using a coarse-to-fine iterative approach. This involves generating a mesh and the weights associating each handle to each vertex in the mesh and iteratively refining the mesh to add resolution until a refinement criteria is satisfied.